1. Field of the Invention
This invention relates to band gap voltage reference circuits and, more particularly, to bandgap voltage reference circuits which are temperature compensated.
2. Description of the Prior Art
Voltage reference circuits have been designed based upon the transistor base-emitter voltage (V.sub.BE) which can be expanded as follows: ##EQU1## where q is the charge of the electron;
k is Boltzmann's constant; PA1 T is the absolute temperature; PA1 V.sub.GO is the semiconductor bandgap voltage extrapolated to absolute zero temperature; V.sub.GO equals 1.240 V for silicon; PA1 .sup.V BEO is the base-emitter voltage at an arbitrarily selected reference temperature To and at the corresponding reference collector current I.sub.CO ; and PA1 n is a parameter which depends upon the type of transistor and process used in manufacturing it.
This voltage, as shown expanded above and gathered into component terms of temperature dependency has a temperature independent term, V.sub.GO, the semiconductor bandgap voltage extrapolated to absolute zero, a term having a first order temperature dependency (T), and a term having a second order temperature dependency (TlnT). The first order temperature dependency term, a much larger term than the second order temperature dependency term, is eliminated by using the differential in base-emitter voltages (.DELTA.V.sub.BE) of two transistors operating at different current densities. ##EQU2## where J1 is the current density of the current through the base-emitter junction of the first transistor and J2 is the current density of the current through the base-emitter junction of the second transistor.
From an examination of the equation above, it can be seen that .DELTA.V.sub.BE is temperature dependent to the first order when the current density ratio J1/J2 is made independent of temperature.
By combining a base-emitter voltage and the differential in base-emitter voltages of two transistors operating at different current densities, a voltage reference having the temperature independent term and the second order term is realized. Heretofore, the second order dependency of such a voltage reference has been ignored, but most recently efforts have been made to eliminate such second order temperature dependency to achieve a temperature independent voltage reference.
One such effort is in U.S. Pat. No. 4,249,122 by Robert J. Wildlar, entitled TEMPERATURE COMPENSATED BANDGAP IC VOLTAGE REFERENCES and issued Feb. 3, 1981. The voltage reference circuit in this patent has a first voltage of the base-emitter voltage of a transistor and a second voltage based on the difference of the base-emitter voltages of two transistors operating at different current densities. The first and second voltage are combined to obtain a resulting voltage which is temperature compensated to the first order. To obtain second order compensation, additional circuitry which is temperature dependent, is used to modify the current densities of the two transistors which generate the difference in base-emitter voltages.
U.S. Pat. No. 4,250,445, entitled BANDGAP REFERENCE WITH CURVATURE CORRECTION, by Adrian P. Brokaw and issued Feb. 10, 1981, discloses another voltage reference circuit having temperature compensation beyond the first order. This circuit employs two transistors operating at different current densities to develop a base-emitter differential voltage. This voltage is combined with a base-emitter voltage of a transistor to attain a first order temperature compensated reference as discussed previously. The improvement lies in a resistor having a certain temperature dependent characteristics so that when the resistor is connected in series with the first order temperature compensated circuit, the second order temperature dependent voltage components are compensated for and the resulting voltage reference has better than first order temperature compensation.
These are some of the more recent efforts to achieve a voltage reference compensated to the second order.